Please answer d) e) f) of the following:

2. Health Insurance, Death Spirals, and Screening: 40 points Pawnee and Eagleton are two neighboring cities with equal population. However, the residents of Eagleton are far more healthy than Pawnee residents. The residents of Eagleton have a 5% probability of requiring medical attention, while this probability for Pawnee residents is 15%. When a person requires medical attention, they must spend 15, 000 to recover, or else they would die. Eagleton residents are also richer than Pawnee residents. Eagleton residents earn a yearly income of $96, 100 and Pawnee residents earn a yearly income of $48,400. The residents of both towns neglect to save, i.e., they spend their entire income on consumption. They all have the same utility u (c) = x/E. (Please provide answers accurate to the second decimal point.) a. What is the expected utility of Pawnee and Eagleton residents without health in- surance? Underline your answers. (2 points) There are competitive health insurance companies selling to residents in both Pawnee and Eagleton. They offer a menu of health insurance contracts. There is the low- deductible contract that covers all medical costs above $3, 000. In essence, the insurance company pays out $12, 000 to their poIiCyholders when they require medical attention (since medical expenditure is $15,000). The other option is the high-deductible con- tract, which covers medical costs above 152:, where x is strictly greater than $3,000 and strictly smaller than $15,000 (15, 000 > x > 3,000). In essence, the insurance company pays out $15, 000 x to their policyholders when they require medical attention. b. What is the actuarially fair premiumthe premium such that insurance compa- nies make zero protfor both contracts sold to Pawnee residents? Underline your answers. (2 points) c. What is the actuarially fair premium for both contracts sold to Eagleton residents? Underline your answers. (2 points) Since insurance companies are competitive, they charge the actuarially fair premium. Furthermore, insurance companies are allowed to discriminate the Pawnee residents from the Eagleton residents, i.e., they can offer differing rates to Pawnee and Eagleton residents. d. What is the expected utility of an insured Pawnee resident under the low-deductible contract and the high-deductible contract, respectively? Underline your answers. (2 points) e. What is the expected utility of an insured Eagleton resident under the low-deductible contract and the high-deductible contract, respectively? Underline your answers. (2 points) f. Which contract would Pawnee and Eagleton residents choose? (1 point)